138756038400 has 1296 divisors, whose sum is σ = 594984918528. Its totient is φ = 30191616000.

The previous prime is 138756038339. The next prime is 138756038401. The reversal of 138756038400 is 4830657831.

138756038400 is a `hidden beast` number, since 1 + 3 + 8 + 7 + 560 + 3 + 84 + 0 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (138756038401) by changing a digit.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 1059206335 + ... + 1059206465.

Almost surely, 2^138756038400 is an apocalyptic number.

138756038400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 138756038400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (297492459264).

138756038400 is an abundant number, since it is smaller than the sum of its proper divisors (456228880128).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

138756038400 is a wasteful number, since it uses less digits than its factorization.

138756038400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 278 (or 256 counting only the distinct ones).

The product of its (nonzero) digits is 483840, while the sum is 45.

The spelling of 138756038400 in words is "one hundred thirty-eight billion, seven hundred fifty-six million, thirty-eight thousand, four hundred".